Question:
$9 x^{2}+6 x+1=0$
Solution:
Given :
$9 x^{2}+6 x+1=0$
$\Rightarrow 9 x^{2}+3 x+3 x+1=0$
$\Rightarrow 3 x(3 x+1)+1(3 x+1)=0$
$\Rightarrow(3 x+1)(3 x+1)=0$
$\Rightarrow 3 x+1=0$ or $3 x+1=0$
$\Rightarrow x=\frac{-1}{3}$ or $x=\frac{-1}{3}$
Hence, $\frac{-1}{3}$ is the root of the equation $9 x^{2}+6 x+1=0$.